A138235 a(n) = floor(n*(6 + sqrt(6))/5).

1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 113, 114

Offset: 1

Author

Reinhard Zumkeller, Mar 07 2008

Keywords

• nonn

Comments

Beatty sequence for (6+sqrt(6))/5; complement of A022840;

a(n) = A138236(A022840(n)) and A138236(a(n)) = A022840(n).

Numbers k such that A248515(k+1) = A248515(k) = least number h such that 1 - h*sin(1/h) < 1/n^2. The difference sequence of A248515 is (0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...), so that A138235 = (1, 3, 5, 6, 8, ...) and A022840 = (2, 4, 7, 9, 12, 14, ...). - Clark Kimberling, Jun 16 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.
• Eric Weisstein's World of Mathematics, Beatty Sequence
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A248515, A022840 (complement).

Programs

Magma

[Floor(n*(6+Sqrt(6))/5): n in [1..70]]; // Vincenzo Librandi, Jun 17 2015

Mathematica

With[{c=6+Sqrt[6]},Table[Floor[(n*c)/5],{n,80}]] (* Harvey P. Dale, Feb 25 2013 *)